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#include <stdio.h>
#include <iostream>
#include <vector>
#include <string.h>
using namespace std;
void package(int *weight,int *size,int n,int c);//构造最优矩阵
void getResult(int n,int c,int *
背包问题是要求一个最优值，如果要求输出这个最优值的方案，可以参照一般动态规划问题输出方案的方法：记录下每个状态的最优值是由哪一个策略推出来的，这样便可根据这条策略找到上一个状态，从上一个状态接着向前推即可。即自顶向下的备忘录法或自底向上。
res
,
int
*
size
,
int
*
weight
);
//构造最优解
int f[10][100];
//构造最优矩阵
int main(){
vector<int> vweight;//定义一个vector数组vweight
vector<int> vsize;
int number;
vweight.push_back(0);
vsize.push_back(0);
cout << "请输入每个物品的重量：";
while (1){
cin >> number;
vweight.push_back(number);//每输入一个数字就把它添加到数组的最后
if (cin.get() == '\n')//如果是回车符则跳出循环
break;
}
int *weight = new int[vweight.size()];//每个物品的重量
if (!vweight.empty()){
memcpy(weight, &vweight[0], vweight.size()*sizeof(int));
}
cout << "请输入每个物品的价值：";
while (1) {
cin >> number;
vsize.push_back(number);
if (cin.get() == '\n')
break;
}
int *size = new int[vsize.size()];//每个物品的价值
if (!vsize.empty()){
memcpy(size, &vsize[0], vsize.size()*sizeof(int));
}
if(vweight.size()!=vsize.size()){
cout << "数据输入错误，请重新开始";
exit(0);
}
cout << "请输入背包的总容量：";
int c; //背包能容的重量
cin >> c;
int n = vweight.size()-1; //物品的个数
int res[n];
for(int a=0;a<n;a++){
res[a]=0;
}
int i,j;
package(weight,size,n,c);
for(i=0;i<=n;i++){
for(j=0;j<=c;j++)
printf("%2d ",f[i][j]);
cout << endl;
}
getResult(n,c,res,size,weight);
cout << "放入背包最大价值: " << f[n][c] << endl;
cout << "放入背包的物品为: ";
for(i=1;i<=n;i++)
if(res[i] == 1)
cout << i << " ";
}
void package(int *weight,int *size,int n,int c){
int i,j;
//初始化矩阵
for(i=1;i<=n;i++)
f[i][0] = 0;
for(j=1;j<=c;j++)
f[0][j] = 0;
for(i=1;i<=n;i++){
for(j=1;j<=c;j++){
//当容量够放入第i个物品，并且放入之后的价值要比不放大
if(weight[i] <= j && f[i-1][j-weight[i]] + size[i] > f[i-1][j]){
f[i][j] = f[i-1][j-weight[i]] + size[i];
}else
f[i][j] = f[i-1][j];
}
}
}
void getResult(int n,int c,int *res,int *size,int *weight){
//构造最优解
int i,j;
j = c;
for(i=n;i>=1;i--){
if(f[i][j] != f[i-1][j]){
res[i] = 1;
j = j - weight[i];
}
}
}